In a large heatproof bowl, combine egg yolks, ¼-cup sugar, and salt. Set the bowl over a saucepan of simmering water. Whisk the mixture until the sugar dissolves and the egg yolks turn to a light-pale yellow color. About 5-6 minutes. Remove from heat and set aside. Allow the mixture to cool. Stir occasionally.
In a large bowl, beat the cream and the rest of the sugar (1/4 cup) until soft peaks form. Add vanilla and mascarpone cheese and continue beating at medium speed until medium peaks form.
Fold the mascarpone mixture with the cool egg yolk mixture until combined and smooth.
Mix espresso with rum.
Assemble the tiramisu. Dip ladyfingers, one at a time in the coffee mixture. Arrange in a single layer at the bottom of a 9x9 square pan. Spread half of the mascarpone cream on top. Dust half of the cocoa powder over it. Repeat process for a second layer of ladyfingers, cream and cocoa.
Refrigerate for at least 4 hours or overnight.